DLASQ1(3)

🦋 DLASQ1(3) — the singular-values girlie 💅

ok so first things first, the manual name situation: this page lives in the Library Functions Manual section 3, and the source file it's documenting is literally

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/dlasq1.f

yes that's the whole NAME section, no cap, that's just how Doxygen do. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DLASQ1 (n, d, e, work, info)

DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. she's a supporting actress but she ATE that role, fr fr. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine DLASQ1 (integer n, double precision, dimension( * ) d, double
    precision, dimension( * ) e, double precision, dimension( * ) work,
    integer info)

so what does she do bestie? DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. that's the whole elevator pitch and honestly it's iconic. ✨

💖 Purpose:

!>
!> DLASQ1 computes the singular values of a real N-by-N bidiagonal
!> matrix with diagonal D and off-diagonal E. The singular values
!> are computed to high relative accuracy, in the absence of
!> denormalization, underflow and overflow. The algorithm was first
!> presented in
!>
!>  by K. V.
!> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
!> 1994,
!>
!> and the present implementation is described in , LAPACK Working Note.
!>

ok the glow-up here: real N-by-N bidiagonal matrix, diagonal D, off-diagonal E, and she computes those singular values to high relative accuracy — but ONLY in the absence of denormalization, underflow and overflow. like, she's accurate, she's not a miracle worker. 😭

the algorithm was first presented by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in , LAPACK Working Note. (the citation slots in the source are lowkey empty, i'm just telling you what's there 🫶)

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🎀 Parameters

• N — N is INTEGER. the number of rows and columns in the matrix. N >= 0. bestie if N is negative we are NOT doing this. 🚫
• D — D is DOUBLE PRECISION array, dimension (N). on entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. on normal exit, D contains the singular values in decreasing order. she reorders, she delivers, she leaves. 💅
• E — E is DOUBLE PRECISION array, dimension (N). on entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. on exit, E is overwritten. overwritten!! like, gone, don't come looking for your old E, she's not coming back. 💀
• WORK — WORK is DOUBLE PRECISION array, dimension (4*N). that's four times N, yes, bring snacks, she needs room. 🍓
• INFO — INFO is INTEGER. the vibe report:
  • = 0: successful exit 🌈 slay
  • < 0: if INFO = -i, the i-th argument had an illegal value 🙈 somebody typed something cursed
  • > 0: the algorithm failed, and here's the breakdown:
    • = 1, a split was marked by a positive value in E
    • = 2, current block of Z not diagonalized after 100*N iterations (in inner while loop). On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into DLASQ1 🔥 (ngl that's kind of a generous failure, she left you the leftovers)
    • = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks) 😭 the outer loop said "no <3"

ok real talk: INFO > 0 means something did go sideways — read which code you got, don't just ignore her. = 2 and = 3 are genuinely different situations. 🫶

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👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 107 of file dlasq1.f.

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⭐ Author (again, yes really)

Generated automatically by Doxygen for LAPACK from the source code. she wasn't written, she was generated. main character energy. 💜

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that's the whole page bestie — LAPACK, Version 3.12.0, dated /home/abui...RC/dlasq1.f(3). mwah, go compute some singular values, ily 🧚💖